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Discover LudwigThe phrase "a second theory" is correct and usable in written English.
You can use it when referring to an additional theory that is being introduced or compared to a first theory.
Example: "After examining the first theory, the researchers decided to explore a second theory that could explain the phenomenon more comprehensively."
Alternatives: "an alternative theory" or "a different theory".
Exact(57)
Which suggests a second theory.
A second theory of reproduction was offered by Aristotle.
A second theory holds that "Hedda" could land at a Shubert house if another show folded.
A second theory holds that innovations in communications and increased surveillance of workers have made life more stressful.
A second theory holds that he suffered from Crohn's disease, although that leaves his skin symptoms largely unexplained.
A second theory is that the pebbles are clods of dust and that the force of the air bag pressing down simply pulverized them.
A second theory relates to the frequency of other sexually transmitted diseases, particularly those that break the skin, thus easing entry of H.I.V.
A second theory, which I examined in a post on Thursday, is that economic anxieties and resentments underpinned the political anger that fuelled the Leave vote.
Similar(3)
A second theory-based approach would be to build upon existing dual process or balance models of work design.
Over a decade ago, we proposed a third theory, that of the 'conformational selection and population shift' [ 4].
That's a sixth theory, I guess.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com